Properties

Label 259182.fh
Number of curves $6$
Conductor $259182$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("259182.fh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259182.fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259182.fh1 259182fh6 [1, -1, 1, -14939559779, -702833547127269] [2] 314572800  
259182.fh2 259182fh4 [1, -1, 1, -935498939, -10937714017557] [2, 2] 157286400  
259182.fh3 259182fh5 [1, -1, 1, -318645779, -25146803187525] [2] 314572800  
259182.fh4 259182fh2 [1, -1, 1, -98798459, 95018511723] [2, 2] 78643200  
259182.fh5 259182fh1 [1, -1, 1, -76495739, 257212812651] [2] 39321600 \(\Gamma_0(N)\)-optimal
259182.fh6 259182fh3 [1, -1, 1, 381058501, 747048148971] [2] 157286400  

Rank

sage: E.rank()
 

The elliptic curves in class 259182.fh have rank \(1\).

Modular form 259182.2.a.fh

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} + 2q^{10} + 2q^{13} - q^{14} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.